Find the value of c and state the amplitude and period of f (?)

the function f is defined, for all values of x, by # f(x) = 2sin (x/3) + c# , where c is a constant. the graph #y = f(x)# passes through the point #( pi/2 , -3 )#

(a) find the value of c
(b) state the amplitude and period of f
(c) sketch the graph of # f(x)# for #0<= x <= 3pi #

1 Answer
Aug 11, 2018

Answer:

Please see the explanation below

Explanation:

The function is

#f(x)=2sin(x/3)+c#

The graph passes through the point #=(pi/2, -3)#

#-3=2*sin(pi/3*1/2)+c#

#-3=2sin(pi/6)+c#

#sin(pi/6)=1/2#

#c+1=-3#

#c=-4#

The value of #c=-4#

The function is

#f(x)=2sin(x/3)-4#

The amplitude is #=2#

The perod is #T=2pi/(1/3)=6pi#

See the graph below

graph{2sin(x/3)-4 [-2.54, 48.76, -12.15, 13.5]}